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Is your model predicting the past?

Moritz Hardt, Michael P. Kim

TL;DR

This work proposes a distinction between these two pathways of prediction, supported by theoretical, empirical, and normative arguments, and derives a meaningful backward baseline for auditing a prediction system as a black box, given only background variables and the system’s predictions.

Abstract

When does a machine learning model predict the future of individuals and when does it recite patterns that predate the individuals? In this work, we propose a distinction between these two pathways of prediction, supported by theoretical, empirical, and normative arguments. At the center of our proposal is a family of simple and efficient statistical tests, called backward baselines, that demonstrate if, and to what extent, a model recounts the past. Our statistical theory provides guidance for interpreting backward baselines, establishing equivalences between different baselines and familiar statistical concepts. Concretely, we derive a meaningful backward baseline for auditing a prediction system as a black box, given only background variables and the system's predictions. Empirically, we evaluate the framework on different prediction tasks derived from longitudinal panel surveys, demonstrating the ease and effectiveness of incorporating backward baselines into the practice of machine learning.

Is your model predicting the past?

TL;DR

This work proposes a distinction between these two pathways of prediction, supported by theoretical, empirical, and normative arguments, and derives a meaningful backward baseline for auditing a prediction system as a black box, given only background variables and the system’s predictions.

Abstract

When does a machine learning model predict the future of individuals and when does it recite patterns that predate the individuals? In this work, we propose a distinction between these two pathways of prediction, supported by theoretical, empirical, and normative arguments. At the center of our proposal is a family of simple and efficient statistical tests, called backward baselines, that demonstrate if, and to what extent, a model recounts the past. Our statistical theory provides guidance for interpreting backward baselines, establishing equivalences between different baselines and familiar statistical concepts. Concretely, we derive a meaningful backward baseline for auditing a prediction system as a black box, given only background variables and the system's predictions. Empirically, we evaluate the framework on different prediction tasks derived from longitudinal panel surveys, demonstrating the ease and effectiveness of incorporating backward baselines into the practice of machine learning.
Paper Structure (45 sections, 7 theorems, 39 equations, 11 figures)

This paper contains 45 sections, 7 theorems, 39 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Our contribution.
  3. Predicting the past.
  4. Backward baselines.
  5. Backward baselines
  6. Backward prediction baseline.
  7. Backward rounding baseline.
  8. Distinguishing forward and backward prediction
  9. Backward prediction as random targeting.
  10. Properties of backward baselines
  11. Basic properties
  12. Rounding recovers optimal backward prediction
  13. Measuring forward predictive power
  14. Backward baselines and demographic parity
  15. Empirical evaluation of backward baselines
  16. ...and 30 more sections

Key Result

Proposition 2

The following properties of backward baselines hold. (a) When $X$ encodes $W$, there exists a predictor $h^*:\mathcal{X} \to \mathcal{Y}$ that achieves loss at most the backward prediction baseline. (b) If $h:\mathcal{X} \to \mathcal{Y}$ is a backward predictor, then its loss is at least the backward baselines. (c) If $h:\mathcal{X} \to \mathcal{Y}$ is a forward predictor, then $g^h$ is com

Figures (11)

  • Figure 1: Example data generating process for covariates $X$, outcome $Y$, and context $W$. Time starts from the left with context $W$ and evolves forward to the right, realizing $X$ then $Y$.
  • Figure 2: Backward baselines on MEPS, columns are different features, rows are different classifiers (random forest, gradient boosting, logistic regression) and metrics (zero-one loss, squared loss, ROC curves). Label $XYY$ denotes standard training and testing, label $WYY$ is the backward prediction baseline, label $WY\hat{Y}$ is the backward rounding baseline. Gray dashed line indicates performance of constant predictor. Error bars represent a standard deviation across $10$ random seeds.
  • Figure 3: Backward baselines on SIPP.
  • Figure 4: Backward baselines on COMPAS
  • Figure 5: Baselines on MEPS for varying features and classifiers (zero-one loss)
  • ...and 6 more figures

Theorems & Definitions (14)

  • Definition 1: Backward and forward prediction
  • Proposition 2
  • Definition 2: Confidence
  • Definition 3: Weak calibration
  • Proposition 3: Informal
  • Proposition 4
  • Proposition : Restatement of Proposition \ref{['prop:basic']}
  • proof : Proof of Proposition \ref{['prop:basic']}
  • Proposition : Formal restatement of Proposition \ref{['prop:gh-equals-gs']}
  • proof : Proof of Proposition \ref{['prop:gh-equals-gs']}
  • ...and 4 more